"Now to the King eternal, immortal, invisible, the only God, be honor and glory for ever and ever. Amen." NIV translation
How could God save the worst of sinners? The simple answer is that He is the King of Kings and a king has the authority to do whatever he wishes. We may often not understand what God is doing or why but, like Paul, we have to understand that He is the King and has the authority. We can hold fast to the knowledge that God always takes care of His people.
"Timothy, my son, I give you this instruction in keeping with the prophecies once made about you, so that by following them you may fight the good fight, holding on to faith and a good conscience." NIV translation
Once again, Paul refers to Timothy as his spiritual son and reminds him that God had led Paul to him. He also reminds him that God has a purpose for him and that is as an example of standing firm in his faith.
The same type of thing happens in our lives, today, if we slow down and pay attention to the people that God brings into our lives. God will bring people into your life to build you up and He will bring others for you to build up in their faith.
"Some have rejected these and so have shipwrecked their faith. Among them are Hymenaeus and Alexander, whom I have handed over to Satan to be taught not to blaspheme." NIV translation
It seems that there were some that were rejecting the spiritual authority of Timothy and therefore that of Paul as well. Although it may seem harsh, we see that Paul has "handed them over to Satan". This is a demonstration of the authority that was given to him in that there was not a "church court" and they did not excommunicate people.